In fact, she told a packed audience at Lisner Auditorium Tuesday, “I went to law school for all the wrong reasons.”

“All of my career has been like that—a lot of serendipity, a lot of chance,” she said.

Justice Kagan retraced the steps of that remarkable career in a relaxed, often funny conversation with George Washington University Law School Professor Bradford R. Clark, a longtime friend. The event, held in honor of Constitution Day, closed the Law School’s 150th anniversary celebration.

“We met when he came to a party at my house,” Justice Kagan said.

“Our parties were not like your parties,” Mr. Clark added hastily to the audience.

Justice Kagan’s second job after graduating from Harvard Law School was as clerk to legendary Justice Thurgood Marshall, the pioneering former civil rights attorney and first African American to serve on the Supreme Court.

It was a “heady experience,” Justice Kagan said.

“[Justice Marshall] was not just a Supreme Court justice,” she said. “He was one of the few people to have served as a Supreme Court justice who would have been in the history books without being a Supreme Court justice. You sit there and you realize that you’re working for one of the icons of American law—a hugely influential figure in American history.”

After her clerkship, Justice Kagan worked for a few years as an associate at D.C. law firm Williams & Connolly, then taught at the University of Chicago Law School. She served as an adviser to President Bill Clinton from 1995 to 1999, first as associate White House counsel and then as deputy assistant to the president for domestic policy and deputy director of the Domestic Policy Council.

Subsequently, she became a visiting professor and, eventually, the first female dean at Harvard Law School.

In 2009, President Obama selected her as the first female solicitor general—the lawyer who argues for the federal government before the country’s highest courts. At the time, Justice Kagan had never before argued a case in an appellate court.

Her first argument was on the government’s behalf in Citizens United v. Federal Election Commission, a landmark campaign finance case before the Supreme Court.

“I have a pretty reasonable opinion of myself—I’m not suffering in the self-esteem department,” she said, remembering the moments before she took the podium. “But my heart was pounding.”

In the end, Justice Kagan had barely finished the first sentence of her argument before the late Justice Antonin Scalia leaned over the bench, booming, “No, no, no, no, no!”

“That kind of got me into it,” she said, laughing.

Justices Kagan and Scalia were close friends until his death in February, going on frequent hunting trips together. Their ideological disagreements, she said, were part of that friendship.

“He was such an extraordinary writer and a powerful thinker,” she said, citing his persuasive advocacy of textualism as a lasting legacy.

Justice Scalia’s famously scathing and eloquent opinions, Justice Kagan said, were written with law students in mind as a principal audience.

“You are the future of the legal profession, so to the extent we can communicate with you, we’re shaping the next generation of legal thought,” she told the audience—a majority of whom were first-year students from GW Law.

Justice Kagan also provided insight into the Supreme Court decision-making process. After each case is argued the justices hold a post-argument conference and, in order of seniority, each casts a non-binding preliminary vote.

Questions from the bench during argument can be “an opportunity to start the conversation I’m going to end at the post conference,” Justice Kagan said. “Sometimes the lawyer is the conduit by which you talk to your colleagues.”

At the end of the conversation, a student asked which case during her time on the bench was, in her opinion, the most consequential.

“Every case is consequential to someone,” Justice Kagan said. “You owe it to that someone to approach everything with a high degree of seriousness.

“Sometimes my clerks, I think, are amused and surprised by this,” she continued. “We’ll spend as much time on some abstruse question of civil procedure that no newspaper is going to report on as we will talking about the case that’s going to land on the front page of the New York Times. And I think that’s the way it should be.”

Justice Kagan’s Advice for Law Students

As GW Law’s 150th anniversary celebrations drew to a close, Supreme Court Justice Elena Kagan offered four pieces of advice to students beginning their legal education.

Try to get to know at least one professor well. Pick someone you like and try to establish a relationship.

It’s not only professors who are going to teach you—it’s your classmates and peers. If your nose is always in a book or you’re always in the library, you’re missing one of the great things about law school.

When you talk to peers, talk to people who don’t share your views. It’s frustrating when people who think the same things stick together. Make sure you’re listening to people who don’t think everything you think.

Even for people with a lot of direction, it’s good to do things off the track you think you’re on. Experiment through law school and be open to unexpected interests and passions.